Dirk Mittenhuber:
New sufficient criteria for the globality of Lie wedges
Journal of Lie Theory, vol. 3 (1), p. 35-45
We consider a simply connected Lie group $G$ with Lie algebra $\lieg$
and Lie semigroups $S,T\subseteq G$ with tangent wedges $\Lie(S)$,
resp. $\Lie(T)$. We give some sufficient conditions for
$W:=\Lie(S)+\Lie(T)$ to be a global Lie wedge.
The first theorem applies to the situation where $G=NH$ is a semidirect
decomposition and $W$ is adapted to this decomposition in the sense
of $\Lie(S)\subseteq\n$ and $\Lie(T)\subseteq\h$ while the second theorem
applies to the case where the semigroup generated by~$S$ and~$T$ admits
a product decomposition $\left< S\cup T \right>=ST$. As an application,
we prove that in a three-dimensional Lie algebra every Lie wedge that lies in t
he
intersection of two distinct halfspace-semialgebras is global in
the corresponding simply connected Lie group.